Fast Adomian Decomposition Method And Its Applications To Nonlinear Systems

The Adomian decomposition method was first introduced by Adomian since the beginning of the 1980's and it could be used to solve the approximate analytic solution of nonlinear differential equations. There are some scholars who show great interest in the decomposition method and it is used for solving a wide range of problems whose mathematical models yield equation or system of equations involving algebraic, differential, integral and integro-differential.In this method the solution is considered as the sum of an infinite series, rapidly converging to an accurate solution. And the the key of the method is how to calculate the Adomian polynomials. There have been several writings of Adomian which describe the decomposition method in detail and apply it to lots of stochastic or deterministic problems.Although the decomposition method can be used to solve some differential equations, there need a great deal of computation in the computating process. In particular, some people cannot complete the computation by themselves when they use the method to solve very complicated problem. So some scholars are studying how to cut down the computation and they have mechanized the decomposition method in Maple. Recently, a new method which could calculate Adomian polynomials was presented by some scholars. The new method can reduce some computation when people use it to solve differential equations. So we call it the fast Adomian decomposition method.In this paper, the author perfects the fast Adomian decomposition method and applies the method to solve more differential equations. Redefine the operator T and its properties and make the method be able to solve system of differential equations. There are two Maple programs which are able to solve some differential equations and systems of differential equations like the fast method. The author validates that the fast method needs less time than the Adomian decomposition method by applying both the fast method's program and the Adomian decomposition method's program to solve the same differential equations.